This invention relates to digital communication systems, and more particularly to the estimation of the sequence of transmitted symbols in such systems.
In EDGE (Enhanced Data Rates for GSM Evolution) cellular communication systems a sequence of symbols is transmitted as an 8 Phase Shift Keying (8-PSK) modulated signal. The signal may propagate along several propagation paths to a receiver. If the time delay between the various propagation paths is comparable to the intersymbol period, then the signal received by the receiver will contain intersymbol interference. The attenuation along each path will vary, as will phase changes due to reflections, so the intersymbol interference will not be merely additive. In addition, the received signal will contain noise, which is assumed to be additive white Gaussian noise.
The receiver must estimate the transmitted sequence of symbols from the received sequence of signal samples. This is assisted by use of a data model. The received signal sample at any discrete time k can be modelled as       x    k    =                              ∑                      j            =            0                    v                ⁢                  xe2x80x83                ⁢                              a            j                    ⁢                      xe2x80x83                    ⁢                      s                          k              -              j                                          +              n        k              ∈    C  
where xk is the received signal sample at time k, v is the number of additional paths being considered by the estimator, aj is the channel impulse response coefficient of the j-th path, skxe2x88x92j is the actual symbol transmitted at time kxe2x88x92j, and nk is the additive white Gaussian noise. The channel impulse response coefficients are determined from training symbols embedded in the transmitted sequence. The receiver knows what transmitted training data to expect, and by comparing the expected training symbols with the training symbols actually received a least squared channel estimator can estimate the channel impulse response coefficients for temporally proximate symbols.
Using vector notation, the data model can be rewritten as
xk=ask+nk
where a=[a0, . . . ,av], and s=[sk, . . . ,skxe2x88x92v]T. N+v consecutive received signal samples can be represented as a vector x=[x1, . . . ,xN+v]T. A stacked data model is then given by
x=As+n
where s=[s1, . . . ,sN]T, n=[n1, . . . ,nN+v]T, and   A  =            [                                                  a              0                                            0                                0                                …                                …                                0                                                              a              1                                                          a              0                                            0                                …                                …                                0                                                              a              2                                                          a              1                                                          a              0                                            …                                …                                0                                                ⋮                                ⋮                                ⋮                                ⋰                                …                                ⋮                                                              a              v                                                          a                              v                -                1                                                                        a                              v                -                2                                                          …                                ⋰                                0                                                0                                ⋮                                ⋮                                …                                …                                ⋮                              ]        ∈          C                        (                      N            +            v                    )                xc3x97        N            
One method of estimating the transmitted sequence of symbols is the Maximum Likelihood Sequence Estimation (MLSE) method. For each of the possible transmitted symbols, the received signal is compared with the signal that should have been received if it was that symbol that had been transmitted. Based on these comparisons, the MLSE method then selects the symbol which was most likely to have been transmitted. The MLSE method is a very accurate sequence estimation method. However, the complexity of the MLSE method is proportional to the number of possible transmitted symbols raised to the power of the number of propagation paths being considered. In EDGE systems there are eight possible transmitted symbols and seven propagation paths are considered, and the complexity of the MLSE method makes it impractical.
A second method of estimating the transmitted symbols is the Zero-Forcing Block Linear Equalizer (ZF-BLE) method. In the ZF-BLE method, the quantity Q is minimized with respect to s, where
Q=∥xxe2x88x92As∥Rnn2,
Rnn=xcex5{nnH} is the covariance matrix of the noise, and the operator xcex5{ } denotes the expectation value. The solution to this minimization is
{circumflex over (s)}=(AHRnnxe2x88x921A)xe2x88x921AHRnnxe2x88x921x
where {circumflex over (s)} is the estimation of the sequence of transmitted symbols s, and AH is the Hermitian (or conjugate transpose) of A.
An improvement over the ZF-BLE method is the Zero-Forcing Block Decision-Feedback Sequence Estimation (ZF-BDFSE) method. The ZF-BDFSE method attempts to simplify the processing required to be carried out by the receiver. The substitution
AHRnnxe2x88x921A=LLH
can be made, where L is a lower triangular matrix, LH is the Hermitian of L, and the product LLH is determined by Cholesky decomposition. The estimated sequence of symbols is then given by
{circumflex over (s)}=Lxe2x88x92HLxe2x88x921AHRnnxe2x88x921x
Although {circumflex over (s)} could be calculated from this expression, the resulting values would lie on a continuum and would generally not match the discrete possible values of the transmitted symbols. However, if a vector z is defined as
z=Lxe2x88x921AHRnnxe2x88x921x
and a difference vector xcex94 is defined as
xcex94=LH{circumflex over (s)}xe2x88x92z
then the estimation of {circumflex over (s)} can be determined by minimizing the magnitude of the difference vector xcex94 with respect to the vector of discrete possible values.
Although the ZF-BDFSE method is less complex than the MLSE method, and has improved performance over the ZF-BLE method, it has a weakness in that a Cholesky decomposition does not always exist. A matrix L can only be found if the channel impulse response correlation matrix is positive definite. To avoid this risk noise can be added to the channel impulse response correlation matrix, but this results in performance degradation. A method is required which does not have the complexity of the MLSE method, which maintains performance improvement over the ZF-BLE method, and for which a solution always exists without having to degrade performance by artificially adding noise.
The present invention provides a method of estimating a transmitted sequence of symbols from a received sequence of signal samples x. Each symbol in the transmitted sequence of symbols is one of a set of discrete possible symbol values. The received sequence of signal samples is a combination of noise having a covariance matrix represented as Rnn and of the transmitted sequence of symbols propagating along at least one path, the paths having a matrix of channel impulse response coefficients represented as A. The method comprises the steps of determining a lower triangular matrix L from the relationship LLH=AHRnnxe2x88x921A+I where I is an identity matrix, calculating a vector z=Lxe2x88x921AHRnnxe2x88x921x, and determining an estimated sequence of symbols {circumflex over (s)} belonging to the set of discrete possible symbol values such that the square of the magnitude of a difference vector LH{circumflex over (s)}xe2x88x92z is minimized. The step of determining the estimated sequence of symbols can be carried out by minimizing each term in the expression for the square of the magnitude of the difference vector successively in order of increasing number of symbols needed to resolve the term. The method can be implemented in a processor in a receiver of a digital communication system.
The method provides improved performance over the ZF-BDFSE method without increasing complexity, thereby improving the quality of the signal or, alternatively, allowing lower mobile transmitted power to be used.
Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures.